Recovering Private Keys Generated with Weak PRNGs

International audienceSuppose that the private key of discrete logarithm-based or factoring-based public-key primitive is obtained by concatenating the outputs of a linear congruential generator. How seriously is the scheme weakened as a result? While linear congruential generators are cryptographically very weak "pseudorandom" number generators, the answer to that question is not immediately obvious, since an adversary in such a setting does not get to examine the outputs of the congruential generator directly, but can only obtain an implicit hint about them—namely the public key. In this paper, we take a closer look at that problem, and show that, in most cases, an attack does exist to retrieve the key much faster than with a naive exhaustive search on the seed of the generator